Title: Physics-Aware Statistical Learning for Scientific Computing and Decision Making in Engineering Applications

Date: July 10th, 2025

Time: 11:50AM-1:50PM EST

Meeting Link: Microsoft Teams Meeting

Xinchao Liu

Ph.D. Candidate in Industrial Engineering

School of Industrial and Systems Engineering

Georgia Institute of Technology

Committee:

Dr. Xiao Liu (Advisor), H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Chuck Zhang (Co-advisor), H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Roshan Joseph, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Shihao Yang, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Levente Klein, IBM TJ Watson Research Center

Abstract:

Motivated by the convergence of physical systems and data-driven technologies under the industry 4.0 paradigm, the research addresses two central challenges: how to emulate nonlinear dynamics governed by physical laws, and how to reduce the cost of sensing and inference in inverse problems. This dissertation investigates physics-aware statistical learning as a principled and computationally efficient framework for modeling complex engineering systems and supporting high-stakes decision-making. By integrating physical knowledge with statistical and machine learning techniques, the proposed approaches enable interpretable, scalable, and uncertainty-aware modeling for scientific computing, advanced manufacturing, and environmental monitoring.

Chapter 2 presents a physics-informed surrogate modeling framework for nonlinear dynamical systems, with a focus on aircraft-UAV collisions. The full-order model derived from finite element analysis (FEA) is computationally expensive, so the proposed method constructs a reduced-order model using proper orthogonal decomposition (POD) and then builds a two-stage statistical model: a multivariate Gaussian process (GP) captures the mapping from collision parameters to external forces, and a function-to-function regression (based on functional principal component analysis) learns the dynamic system response. The resulting surrogate achieves reasonable prediction accuracy while offering great speed-up compared to direct FEA, making it a practical tool for assessing collision severity under varying impact conditions. We show that the proposed physics-informed statistical model can achieve a 12% out-of-sample mean relative error, and is more than 10^3 times faster than Finite Element Analysis (FEA).

Chapter 3 addresses the inverse problem of ultrasonic weak bond detection in advanced manufacturing. We propose a physics‑aware statistical ML framework for ultrasound testing and evaluation: combining function‑to‑function Gaussian Process regression with Amortized Variational Inference to estimate latent physical variables reflecting adhesive bond integrity and strength. This approach integrates rich functional data with physical modeling for robust integrity assessment. The method enables estimation of interfacial stiffness from large-volume ultrasound data while mitigating the effects of ultrasonic couplants and measurement artifacts. By incorporating frequency-domain information and enforcing smoothness in the inference network, the model achieves physically interpretable and real-time estimations of bond quality. Validation on both simulated and experimental data demonstrates the method’s ability to perform scalable and accurate inspections, providing a valuable tool for nondestructive evaluation and quality assurance in adhesive-bonded structures.

Chapter 4 focuses on sparse sensor allocation for detecting leaking emission sources, such as methane, over large spatial domains. The problem is formulated as a bilevel optimization where the upper-level objective minimizes the integrated mean squared error (IMSE) of estimated emission rates, while the lower level solves a constrained inverse problem accounting for non-negativity, sparsity, and physical uncertainties such as wind conditions. Two solution algorithms are proposed: repeated sample average approximation (rSAA) and stochastic bilevel approximation (SBA). The framework significantly improves inference accuracy and adapts sensor deployment based on underlying physics and uncertainty, demonstrating its utility in environmental monitoring and smart sensing systems. Convergence analysis is performed to obtain the performance guarantee, and comprehensive numerical investigations show that the proposed approach can allocate sensors according to the parameters and output of the forward model. Computationally efficient code with GPU acceleration is developed. Lastly, Chapter 5 summarizes the original contributions of this dissertation and outlines future research directions.